The fact that Seesaw enables and encourages parents to interact with their child's LJ posts and your class blog posts is fantastic, but having to constantly approve them all can get a little tedious.
If this is the case, just open up Manage Class and tweak the notification settings, so you don't need to approve them. Don't panic; when you open up Seesaw you will see a stream of the comments that have been added, any of which you can remove in the highly unlikely event that any of them are inappropriate:
It's OK, you can kill those as well: Account Settings > there's a few useful things to check here, but in particular the ability to switch off email notifications, or to have them arrive as one email digest a day.